Recall that the longest-probe bound in open addressing is the maximum number of probes required to find an empty slot or a key during a search operation.

Consider the worst-case scenario where all keys hash to the same index, forcing a linear probe sequence; analyze how this affects the bound.

Derive the upper bound for the longest-probe sequence by modeling the hash table as a sequence of occupied and empty slots, then applying combinatorial analysis to determine the maximum possible probe length.